Geometry

Question Analysis

The main focus is to determine if a given point  lies on a circle. We first need to find the center and radius of the circle using the endpoints of the diameter  and , and then check if the distance from the center to point  is equal to the radius.

 

Key Concept Explanation

1. The center of a circle with diameter endpoints  and  is the mid - point, given by the formula .

2. The radius  of a circle is the distance from the center  to any point  on the circle. The distance formula is . If the distance from the center to a point is equal to the radius, then the point lies on the circle.

 

Step - by - Step Solution

1. Find the center of the circle:

Given  and , the center  of the circle (mid - point of ) is

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